The Stability of many-particle systems

THEORIE QUANTIQUE

PHYSIQUE

STABILITE

Abstract : It is shown that a quantal or classical system of N particles of distinct species ?,? = 1, 2, … ? interacting through pair potentials ???(r) are stable, in the sense that the total energy is always bounded below by ?NB, provided ???(r) exceeds some ???(2)(r) whose Fourier transform ????(p)????(p) corresponds to a positive semidefinite ? × ? matrix for all p.

This result is applied to discuss charged systems and stability is proved for Coulomb interactions if the charges are somewhat smeared rather than concentrated at points. For a large class of potentials it is shown that classical instability implies quantum instability in the case of bosons and, in three or more dimensions, also of fermions. Quantum systems with Coulomb interactions (point charges) are discussed and it is shown in particular that their stability cannot depend on the ratios between the masses of the particles.

This result is applied to discuss charged systems and stability is proved for Coulomb interactions if the charges are somewhat smeared rather than concentrated at points. For a large class of potentials it is shown that classical instability implies quantum instability in the case of bosons and, in three or more dimensions, also of fermions. Quantum systems with Coulomb interactions (point charges) are discussed and it is shown in particular that their stability cannot depend on the ratios between the masses of the particles.

RUELLE

FISHER

P/65/03

IHES

1965

A4

17 f.

EN

TEXTE

PREPUBLICATION

P_65_03.pdf

1965

IHES

IHES

RUELLE

FISHER

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/RUELLE/1965-1976/P_65_03/P_65_03.pdf

Oui

Bures-sur-Yvette

COULOMB

FOURIER

DOBRUSHIN

YUKAWA

HERMITE

BOSE

EINSTEIN

BOLTZMANN

FERMI

DIRAC

HAMILTON

HILBERT